Single- and Multiple-Shell Uniform Sampling Schemes for Diffusion MRI Using Spherical Codes

Area of Science:

• Medical Imaging
• Neuroscience
• Computational Physics

Background:

• Diffusion MRI (dMRI) relies on effective sampling schemes for efficient data acquisition and accurate reconstruction.
• Current methods like Generalized Electrostatic Energy Minimization (GEEM) are used but do not directly optimize for maximal angular separation between sampling points.

Purpose of the Study:

• To introduce a novel formulation, Spherical Code (SC), for designing optimal single and multi-shell dMRI sampling schemes.
• To directly maximize the minimal angle between sampling points, enhancing rotational invariance and data quality.

Main Methods:

• Developed the Spherical Code (SC) formulation for continuous and discrete sampling problems in dMRI.
• Proposed five algorithms: Incremental SC (ISC), Iterative Maximum Overlap Construction (IMOC), 1-Opt greedy, Mixed Integer Linear Programming (MILP), and Constrained Non-Linear Optimization (CNLO).
• Applied SC to design and optimize sampling schemes for dMRI acquisition.

Main Results:

• SC methods achieved greater angular separation between sampling points compared to EEM and GEEM.
• Demonstrated superior rotational invariance properties with SC-designed sampling schemes.
• Experimental results validated the effectiveness of SC in improving dMRI sampling.

Conclusions:

• The Spherical Code formulation provides a more direct and effective approach to optimizing dMRI sampling schemes.
• SC methods offer significant advantages in angular separation and rotational invariance over existing state-of-the-art techniques.
• The developed algorithms and released codes (DMRITool) facilitate the practical application of SC in dMRI research.